# One Way ANOVA and Normality

#### AEGomes

##### New Member
Hi everyone!
Considering a sample with n=37 504.
The Normality hypothesis is rejected.
Is it safe to performe One Way ANOVA test?
Thank you!

#### Karabiner

##### TS Contributor
With such a huge sample, why do you want to perform a test?!
How many subgroups are there?

#### AEGomes

##### New Member
Within this sample (with n=37 504) need to compare 6 subgroups:
1-n=12544
2-n=12480
3-n=5120
4-n=2240
5-n=2048
6-n=3072
How can I compare those subgroups?
Thank you!

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#### Karabiner

##### TS Contributor
Normality tests (H0: "the distribution is exactely normal in the population from
which the data are sampled") always show deviations from normality, if sample size
is so large. Mind that for linear regression or analysis of variance, not the dependent
variable should be normally distributed, but the prediction errors from the model (the
residuals). But you can safely ignore this if sample size is large (n > 50 or so).
So you can do a oneway ANOVA here. The question remains, why you want
to do an analysis with such a huge sample size. Even in the smallest subgroup here,
the standard error of the mean is very tiny ( SD / 45 for n=2048), so you could
just use the descriptive statistics. p-values tell you nothing about the size or
relevance of an effect.

With kind regards

Karabiner

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#### fed2

##### Active Member
. p-values tell you nothing
you could say that with smaller sample sizes. maybe they are just needed to pay lip service to thestats gods. thats where most of em come from anyway.